Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5

Question

feet and a standard deviation of 0.5
feet. A sample of 51
men’s step lengths is taken.
Step 2 of 2: Find the probability that the mean of the sample taken is less than 1.9
feet. Round your answer to 4
decimal places, if necessary.

Answer 1

To find the probability that the mean of the sample taken is less than 1.9 feet, we first need to calculate the standard error of the mean:

Standard Error = standard deviation / sqrt(sample size)
Standard Error = 0.5 / sqrt(51)
Standard Error ≈ 0.0707

Next, we calculate the z-score for the sample mean of 1.9 feet:

z = (sample mean - population mean) / standard error
z = (1.9 - 2.5) / 0.0707
z ≈ -8.47

Using a standard normal distribution table or calculator, we find the probability that z is less than -8.47 is approximately 0.0000.

Therefore, the probability that the mean of the sample taken is less than 1.9 feet is 0.0000.